Multiple-criteria decision making: concepts, techniques, and extensions
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York, NY [u.a.]
Plenum Pr.
1985
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| Series: | Mathematical concepts and methods in science and engineering
30 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 388 S. graph. Darst. |
| ISBN: | 0306419653 |
Staff View
MARC
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| 245 | 1 | 0 | |a Multiple-criteria decision making |b concepts, techniques, and extensions |c Po-Lung Yu |
| 264 | 1 | |a New York, NY [u.a.] |b Plenum Pr. |c 1985 | |
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Record in the Search Index
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| adam_text | Contents
1. Introduction 1
1.1. The Needs and Basic Elements 1
1.2. An Overview of the Book 2
1.3. Notation 4
2. Binary Relations 7
2.1. Preference as a Binary Relation 7
2.2. Characteristics of Preferences 11
2.3. Optimality Condition 14
2.4. Further Comments 16
Exercises 16
3. Pareto Optimal or Efficient Solutions 21
3.1. Introduction 21
3.2. General Properties of Pareto Optimal Solutions 22
3.3. Conditions for Pareto Optimality in the Outcome Space .... 24
3.3.1. Conditions for a General Y 24
3.3.2. Conditions when Y Is As Convex 25
3.3.3. Boundedness of Tradeoff and Proper Efficiency 28
3.4. Conditions for Pareto Optimality in the Decision Space .... 32
3.4.1. Conditions in Terms of Single Criterion Maximization . . 32
3.4.2. Conditions in Terms of Differentiability 35
3.4.3. Decomposition Theorems of X°( ) and X°(A ) .... 38
3.4.4. An Example 40
3.5. Further Comments 49
3.6. Appendix: Generalized Gordon Theorem 49
3.7. Appendix: Optimality Conditions 49
Exercises 51
4. Goal Setting and Compromise Solutions 55
4.1. Introduction 55
xi
xii Contests
4.2. Satisficing Solutions 56
4.2.1. Goal Setting 56
4.2.2. Preference Ordering and Optimality in Satisficing Solutions 58
4.2.3. Mathematical Programs and Interactive Methods 60
4.3. Compromise Solutions 66
4.3.1. Basic Concepts 67
4.3.2. General Properties of Compromise Solutions 71
4.3.3. Properties Related to p 74
4.3.4. Computing Compromise Solutions 81
4.3.5. Interactive Methods 89
4.4. Further Comments 91
Exercises 92
5. Value Function 95
5.1. Revealed Preference from a Value Function 96
5.2. Conditions for Value Functions to Exist 98
5.3. Additive and Monotonic Value Functions and Preference
Separability 100
5.3.1. Additive and Monotonic Value Functions and Implied
Preference Separability 101
5.3.2. Conditions for Additive and Monotonic Value Functions 103
5.3.3. Structures of Preference Separability and Value Functions 106
5.4. Further Comments 109
Exercises 110
6. Some Basic Techniques for Constructing Value Functions 113
6.1. Constructing General Value Functions 114
6.1.1. Constructing Indifference Curves (Surfaces) 114
6.1.2. Constructing the Tangent Planes and the Gradients of Value
Functions 116
6.1.3. Constructing the Value Function 117
6.2. Constructing Additive Value Functions 119
6.2.1. A First Method for Constructing Additive Value Functions 120
6.2.2. A Second Method for Constructing Additive Value Functions 122
6.3. Approximation Method 125
6.3.1. A General Concept 125
6.3.2. Approximation for Additive Value Functions 126
6.3.3. Eigenweight Vectors for Additive Value Functions .... 133
6.3.4. Least Distance Approximation Methods 142
6.4. Further Comments 155
6.5. Appendix: Perron Frobenius Theorem 156
Exercises 156
7. Domination Structures and Nondominated Solutions 163
7.1. Introduction 163
7.2. Domination Structures 164
Contents xiii
7.3. Constant Dominated Cone Structures 168
7.3.1. Cones and their Polars 169
7.3.2. General Properties of TV Points 171
7.3.3. A Characterization of TV Points 175
7.3.4. Cone Convexity and TV Points 177
7.3.5. TV Points in the Decision Space 184
7.3.6. Existence, Properness, and Duality Questions 187
7.4. Local and Global TV Points in Domination Structures 188
7.5. Interactive Approximations for TV Points with Information
from Domination Structures 195
7.6. Further Comments 204
7.7. Appendix: A Constructive Proof of Theorem 7.3 205
Exercises 210
8. Linear Cases, MC and MC2 Simplex Methods 215
8.1. TV Points in the Linear Case 215
8.2. MC Simplex Method and TVcx Points 219
8.2.1. MC Simplex Method and Set of Optimal Weights .... 219
8.2.2. Decomposition of the Weight Space 226
8.2.3. Connectedness and Adjacency of TV^ Points, and a Method for
Locating Nell Set 231
8.3. Generating the Set TV from TVcx Points 234
8.3.1. The Need for the Entire Set TV 234
8.3.2. Decomposition of the Set TV into Nondominated Faces . . 235
8.3.3. Method to Locate All TV Faces and Examples 239
8.4. MC2 Simplex Method and Potential Solutions in Linear Systems 243
8.4.1. Introduction 243
8.4.2. Potential Solutions of Linear Systems 244
8.4.3. The MC2 Simplex Method 246
8.4.4. Separation, Adjacency, and Connectedness 249
8.4.5. Duality of MC2 Programs 255
8.4.6. An Example 258
8.5. Further Comments 263
8.6. Appendix: Proof of Lemma 8.2 264
Exercises . . . 266
9. Behavioral Bases and Habitual Domains of Decision Making 271
9.1. Introduction 271
9.2. Behavioral Bases for Decision Making 273
9.2.1. A Model for Decision/Behavior Processes—Overview . . 273
9.2.2. Internal Information Processing Center—The Brain . . . 275
9.2.3. Goal Setting, Self Suggestion, and State Valuation .... 277
9.2.4. Charge Structures and Significance Ordering of Events . . 280
9.2.5. Least Resistance Principle, Discharge, and Problem Solving 287
9.2.6. External Information Inputs 289
9.3. Habitual Domains 291
9.3.1. Definition and Formation of Stable Habitual Domains . . 292
xiv Contents
9.3.2. The Expansion of Habitual Domains 294
9.3.3. Interaction of Different Habitual Domains 299
9.3.4. Implications of Studying Habitual Domains 301
9.4. Some Observations in Social Psychology 303
9.4.1. Social Comparison Theory 303
9.4.2. Halo Effect 303
9.4.3. Projection Effect (Assumed Similarity) 304
9.4.4. Proximity Theory 304
9.4.5. Reciprocation Behaviors 304
9.4.6. Similarity Effect 305
9.4.7. Scapegoating Behavior (Displacement of Aggression) . . . 305
9.4.8. Responsibility Diffusion or Deindividuation in Group
Behavior 305
9.5. Some Applications 305
9.5.1. Self Awareness, Happiness, and Success 306
9.5.2. Decision Making 308
9.5.3. Persuasion, Negotiation, and Gaming 309
9.5.4. Career Management 310
9.6. Further Comments 312
9.7. Appendix: Existence of Stable Habitual Domains 312
Exercises 321
10. Further Topics 325
10.1. Interactive Methods for Maximizing Preference Value Functions 325
10.1.1. Adapted Gradient Search Method 326
10.1.2. Surrogate Worth Tradeoff Method 327
10.1.3. Zionts Wallenius Method 331
10.2. Preference over Uncertain Outcomes 333
10.2.1. Stochastic Dominance (Concepts Based on CDF) ... 333
10.2.2. Mean Variance Dominance (Concepts Based on Moments) 334
10.2.3. Probability Dominance (Concept Based on Outperforming
Probability) 334
10.2.4. Utility Dominance (Concept Based on Utility Functions) 335
10.2.5. Some Interesting Results 335
10.3. Multicriteria Dynamic Optimization Problems 336
10.3.1. Finite Stage Dynamic Programs with Multicriteria . . . 336
10.3.2. Optimal Control with Multicriteria 342
10.4. Second Order Games 348
10.4.1. Decision Elements and Decision Dynamics 349
10.4.2. Second Order Games 352
10.4.3. Second Order Games and Habitual Domains 355
Exercises 357
Bibliography 361
Index 383
|
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| indexdate | 2024-07-09T15:43:28Z |
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| isbn | 0306419653 |
| language | English |
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| physical | XIV, 388 S. graph. Darst. |
| publishDate | 1985 |
| publishDateSearch | 1985 |
| publishDateSort | 1985 |
| publisher | Plenum Pr. |
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| series | Mathematical concepts and methods in science and engineering |
| series2 | Mathematical concepts and methods in science and engineering |
| spelling | Yu, Po-lung 1940- Verfasser (DE-588)170065081 aut Multiple-criteria decision making concepts, techniques, and extensions Po-Lung Yu New York, NY [u.a.] Plenum Pr. 1985 XIV, 388 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematical concepts and methods in science and engineering 30 Multikriteria-Entscheidung Statistische Entscheidungstheorie (DE-588)4077850-2 gnd rswk-swf Entscheidungstheorie (DE-588)4138606-1 gnd rswk-swf Statistische Entscheidungstheorie (DE-588)4077850-2 s DE-604 Entscheidungstheorie (DE-588)4138606-1 s Mathematical concepts and methods in science and engineering 30 (DE-604)BV000001144 30 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Yu, Po-lung 1940- Multiple-criteria decision making concepts, techniques, and extensions Mathematical concepts and methods in science and engineering Multikriteria-Entscheidung Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| subject_GND | (DE-588)4077850-2 (DE-588)4138606-1 |
| title | Multiple-criteria decision making concepts, techniques, and extensions |
| title_auth | Multiple-criteria decision making concepts, techniques, and extensions |
| title_exact_search | Multiple-criteria decision making concepts, techniques, and extensions |
| title_full | Multiple-criteria decision making concepts, techniques, and extensions Po-Lung Yu |
| title_fullStr | Multiple-criteria decision making concepts, techniques, and extensions Po-Lung Yu |
| title_full_unstemmed | Multiple-criteria decision making concepts, techniques, and extensions Po-Lung Yu |
| title_short | Multiple-criteria decision making |
| title_sort | multiple criteria decision making concepts techniques and extensions |
| title_sub | concepts, techniques, and extensions |
| topic | Multikriteria-Entscheidung Statistische Entscheidungstheorie (DE-588)4077850-2 gnd Entscheidungstheorie (DE-588)4138606-1 gnd |
| topic_facet | Multikriteria-Entscheidung Statistische Entscheidungstheorie Entscheidungstheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001505021&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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